InterviewSolution
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InterviewSolution
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Let ` vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i- hat j- hat k`be three vectors. A vector ` vec v`in the plane of ` vec aa n d vec b ,`whose projection on ` vec c`is `1/(sqrt(3))`is given by` hat i-3 hat j+3 hat k`b. `-3 hat i-3 hat j+3 hat k`c. `3 hat i- hat j+3 hat k`d. ` hat i+3 hat j-3 hat k`A. `hat(i)-3hat(j)+3hat(k)`B. `-3hat(i)-3hat(j)-hat(k)`C. `3hat(i)-hat(j)+3hat(k)`D. `hat(i)+3hat(j)-3hat(k)` |
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Answer» Correct Answer - C Let `vec(v)= vec(a) +lambda vec(b)` `vec(b) =(1 + lambd) hat(i) +(1-lambda) hat(j) (1+lambda) hat(k)` Projection of `vec(v) " on " vec(c ) = (1)/(sqrt(3)) rArr (vec(v).vec(c ))/(|vec(c )|) = (1)/(sqrt(3))` `rArr ((1+lambda)-(1-lambda)-(1+lambda))/(sqrt(3)) =(1)/(sqrt(3))` `rArr 1+lambda -lambda -1 +lambda -1 -lambda =1` `rArr vec(v) =3 hat(i) - hat(j) + 3hat(k)` |
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